A025803 Expansion of 1/((1-x^2)*(1-x^4)*(1-x^7)).

1, 0, 1, 0, 2, 0, 2, 1, 3, 1, 3, 2, 4, 2, 5, 3, 6, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 13, 9, 14, 10, 16, 11, 17, 13, 19, 14, 20, 16, 22, 17, 24, 19, 26, 20, 28, 22, 30, 24, 32, 26, 34, 28, 36, 30, 39, 32, 41, 34, 44, 36, 46, 39

Offset

0,5

Comments

a(n) is the number of partitions of n into parts 2, 4, and 7. - Hoang Xuan Thanh, Jun 18 2025

Links

Table of n, a(n) for n=0..63.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1,1,0,-1,0,-1,0,1).

Formula

a(n) = floor((n^2 + n*(13+7*(-1)^n) + 90 + 50*(-1)^n)/112). - Hoang Xuan Thanh, Jun 18 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^4)(1-x^7)), {x, 0, 100}], x] (* Harvey P. Dale, Jan 17 2021 *)

Crossrefs

Sequence in context: A237184 A029240 A302642 * A029185 A029184 A179049

Adjacent sequences: A025800 A025801 A025802 * A025804 A025805 A025806

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved